A mechanical system model is derived as \(m \ddot{x}+b \dot{x}+k x=f(t)\), where \(m=2, b=\frac{1}{2}\), \(k=5\), and applied force \(f(t)=\frac{2}{5} e^{-t}\), all in consistent physical units. The system is subjected to zero initial conditions. Assuming that \(x\) is the output, find the transfer function.